| Title:
|
About $wcs$-covers and $wcs^*$-networks on the Vietoris hyperspace $\mathcal F(X)$ (English) |
| Author:
|
Tuyen, Luong Q. |
| Author:
|
Tuyen, Ong V. |
| Author:
|
Tuan, Phan D. |
| Author:
|
Truc, Nguzen X. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
64 |
| Issue:
|
4 |
| Year:
|
2023 |
| Pages:
|
519-527 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study some generalized metric properties on the hyperspace $\mathcal F(X)$ of finite subsets of a space $X$ endowed with the Vietoris topology. We prove that $X$ has a point-star network consisting of (countable) $wcs$-covers if and only if so does $\mathcal F(X)$. Moreover, $X$ has a sequence of $wcs$-covers with property $(P)$ which is a point-star network if and only if so does $\mathcal F(X)$, where $(P)$ is one of the following properties: point-finite, point-countable, compact-finite, compact-countable, locally finite, locally countable. On the other hand, $X$ has a $wcs^*$-network with property $\sigma$-$(P)$ if and only if so does $\mathcal F(X)$. By these results, we obtain some results related to the images of metric spaces and separable metric spaces under some kinds of continuous mappings on the Vietoris hyperspace $\mathcal F(X)$. (English) |
| Keyword:
|
hyperspace |
| Keyword:
|
generalized metric property |
| Keyword:
|
$wcs$-cover |
| Keyword:
|
$wcs^*$-network |
| MSC:
|
54B20 |
| MSC:
|
54C10 |
| MSC:
|
54D20 |
| MSC:
|
54E40 |
| idZBL:
|
Zbl 07953697 |
| idMR:
|
MR4813801 |
| DOI:
|
10.14712/1213-7243.2024.011 |
| . |
| Date available:
|
2024-11-05T11:54:58Z |
| Last updated:
|
2026-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152619 |
| . |
| Reference:
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